This line crosses the point (4,5)so we can make an equation to find the slope:
![4 = a \times 5 \\ 4 = 5a \\ a = \frac{4}{5}](https://tex.z-dn.net/?f=4%20%3D%20a%20%5Ctimes%205%20%5C%5C%204%20%3D%205a%20%5C%5C%20%20a%20%3D%20%20%5Cfrac%7B4%7D%7B5%7D%20)
hope this helps
Answer:
V = 5280 in^3
Step-by-step explanation:
The volume is found by
V = Bh where B is the area of the base and h is the height
first we need to find the area of the base
The base is the triangle
We need to find the base dimension for the triangle
34^2 = 16^2 + b^2
34^2 -16^2 = b^2
900 = b^2
30 =b
B = 1/2 bh
= 1/2 (30) *16
B =240
V = Bh
V = 240 * 22
V = 5280 in^3
Answer
Find out the what fraction of the sandcastle did they build together .
To prove
Let us assume that the fraction of the sandcastle they build together be x .
As given
![Beatrice\ built\ about\ \frac{1}{3}\ of\ a\ sandcastle.](https://tex.z-dn.net/?f=Beatrice%5C%20built%5C%20about%5C%20%5Cfrac%7B1%7D%7B3%7D%5C%20of%5C%20a%5C%20sandcastle.)
![Linda\ built\ \frac{4}{7}\ of\ the\ same\ castle.](https://tex.z-dn.net/?f=Linda%5C%20built%5C%20%5Cfrac%7B4%7D%7B7%7D%5C%20of%5C%20the%5C%20same%5C%20castle.)
Than the equation becomes
![x = \frac{1}{3} +\frac{4}{7}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2B%5Cfrac%7B4%7D%7B7%7D)
L.C .M of (3,7) = 21
solving
![x = \frac{7 + 3\times4}{21}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B7%20%2B%203%5Ctimes4%7D%7B21%7D)
![x = \frac{19}{21}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B19%7D%7B21%7D)
Therefore the fraction of the sandcastle did they build together be
![x = \frac{19}{21}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B19%7D%7B21%7D)
Hence proved
Answer:
Test scores of 10.2 or lower are significantly low.
Test scores of 31 or higher are significantly high
Step-by-step explanation:
Z-score:
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
![\mu = 20.6, \sigma = 5.2](https://tex.z-dn.net/?f=%5Cmu%20%3D%2020.6%2C%20%5Csigma%20%3D%205.2)
Significantly low:
Z-scores of -2 or lower
So scores of X when Z = -2 or lower
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-2 = \frac{X - 20.6}{5.2}](https://tex.z-dn.net/?f=-2%20%3D%20%5Cfrac%7BX%20-%2020.6%7D%7B5.2%7D)
![X - 20.6 = -2*5.2](https://tex.z-dn.net/?f=X%20-%2020.6%20%3D%20-2%2A5.2)
![X = 10.2](https://tex.z-dn.net/?f=X%20%3D%2010.2)
Test scores of 10.2 or lower are significantly low.
Significantly high:
Z-scores of 2 or higher
So scores of X when Z = 2 or higher
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![2 = \frac{X - 20.6}{5.2}](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7BX%20-%2020.6%7D%7B5.2%7D)
![X - 20.6 = 2*5.2](https://tex.z-dn.net/?f=X%20-%2020.6%20%3D%202%2A5.2)
![X = 31](https://tex.z-dn.net/?f=X%20%3D%2031)
Test scores of 31 or higher are significantly high